Also, Bethenny said that she doesn't have a nanny, just a housekeeper who sometimes also babysits so Beth didn't want to make her stay too late. Lu kept saying, "What are you going to do, watch her sleep?" Uh, yeah. Not literally watch her, but its not like you can just leave an 8 year old home asleep alone.
ETA: About the stove (and dishwasher) in the bedroom. The only explanation that make sense to me is that the room must have been rented out as some kind of airbnb by the previous owner. It probably wouldn't make any financial sense for Lu to tear it out because the rental potential adds value to the house. If Lu is smart, she will rent it out sometimes when she won't be there.